Question

Which is equal to ^6 sqrt 48^3?

Answer 1

\(\Large \bf \sqrt[6]{48^3}\quad ?\)

Answer 2

yes thats right.

Answer 3

\(\bf \Large {{\color{blue}{ 48\implies 2\cdot 2\cdot 2\cdot 2\cdot 3\implies 2^2\cdot 2^2\cdot 3}}
\\ \quad \\ \quad \\

\sqrt[6]{48^3}\implies \sqrt[6]{(2^2\cdot 2^2\cdot 3)^3}\implies \sqrt[6]{2^{2\cdot 3}\cdot 2^{2\cdot 3}\cdot 3^3}}\)

what do you think?

Answer 4

Honestly I dont know...

Answer 5

\[2\sqrt{6}?\]

Answer 6

\(\Large \bf {{\color{blue}{ 48\implies 2\cdot 2\cdot 2\cdot 2\cdot 3\implies 2^2\cdot 2^2\cdot 3}}
\\ \quad \\ \quad \\

\sqrt[6]{48^3}\implies \sqrt[6]{(2^2\cdot 2^2\cdot 3)^3}\implies \sqrt[6]{2^{2\cdot 3}\cdot 2^{2\cdot 3}\cdot 3^3}
\\ \quad \\
\sqrt[{\color{red}{ 6}}]{2^{\color{red}{ 6}}\cdot 2^{\color{red}{ 6}}\cdot 3^3}\implies 2\cdot 2\sqrt[{\color{red}{ 6}}]{3} }\)

anything that matches the radical, or root, comes out, losing their exponents, thus

Answer 7

ok...

Answer 8

so, just multiply the two fellows that came out
and you'd get the value in front of the radical

Answer 9

so, \[4^6 \sqrt{3}\]

Answer 10

or what?

Answer 11

\(\Large \bf \sqrt[{\color{red}{ 6}}]{2^{\color{red}{ 6}}\cdot 2^{\color{red}{ 6}}\cdot 3^3}\implies 2\cdot 2\sqrt[{\color{red}{ 6}}]{3} \implies 4\sqrt[6]{3}\)

Answer 12

ok what is the next step...? the exponents?

Answer 13

that's as simplified as you can get it

Answer 14

so then is it option C? \[4\sqrt{6}\]

Answer 15

because there are no options that say \[4\sqrt[6]{3}\]

Answer 16

hmmm those options don't show any \(\Large \sqrt[6]{\qquad }\)

Answer 17

nope

Answer 18

so I wonder if the original included \(\Large \sqrt[6]{\qquad }\) or was it just \(\Large \sqrt[]{\qquad }\)

Answer 19

hmmm oh and even then I forgot the 3 has a exponent anyway, should be \(\Large \bf \sqrt[{\color{red}{ 6}}]{2^{\color{red}{ 6}}\cdot 2^{\color{red}{ 6}}\cdot 3^3}\implies 2\cdot 2\sqrt[{\color{red}{ 6}}]{3^3} \implies 4\sqrt[6]{3^3} \)

Answer 20

original problem was\[\sqrt[6]{48^{3}}\]

Answer 21

hmmm I see

ok.... so \(\Large { \bf \sqrt[{\color{red}{ 6}}]{2^{\color{red}{ 6}}\cdot 2^{\color{red}{ 6}}\cdot 3^3}\implies 2\cdot 2\sqrt[{\color{red}{ 6}}]{3^3} \implies 4\sqrt[6]{3^3}
\\ \quad \\
\textit{keep in mind that } \sqrt[{\color{red} m}]{a^{\color{blue} n}}=a^{\frac{{\color{blue} n}}{{\color{red} m}}}\qquad thus
\\ \quad \\

4\sqrt[{\color{red}{ 6}}]{3^{\color{blue}{ 3}}}\implies 4\cdot 3^{\frac{{\color{blue} 3}}{{\color{red} 6}}}\implies 4\cdot 3^{\frac{1}{2}}
\\ \quad \\
\implies 4\sqrt[{\color{red}{ 2}}]{3^{\color{blue}{ 1}}}\implies 4\sqrt{3}}\)

Answer 22

thank you:)

Answer 23

yw